There’s a lot of scholarship on this, and it seems like a lot of symbolism was acquired after the fact, but basically the earliest known writings require that it include two cooked dishes. But the limitations on cooking on the sabbath meant it was more convenient to cook the dish the day before. Eggs are plentiful in the spring, and a boiled egg will keep a few days while not running afoul of sabbath restrictions.
Over time it picked up a lot of other symbolic interpretations, but was basically a consequence of religious laws governing foodways on specific days.
Similar to how Easter eggs were originally a consequence of medieval church restrictions on eating eggs during lent, but the chickens didn’t know to stop laying, you could avoid quite a bit of waste by boiling them a few days before Easter and then feasting on them. And then over time, all sorts of other symbolism was retroactively attributed to it. But it was originally mostly about religious restrictions on how to prepare and use foods during certain times or events.